Question

The algebraic expression of an arithmetic sequence is 3-5n ?
Find its common difference?
Find its first term?
Form a sequence ?

Answer 1

ANSWER:

• 3 - 5n forms an A.P

• First term = - 2

• Common difference = - 5

• Sequence : -2 , -7 , - 12, - 17, ...........

TO FIND:

• If 3 - 5n forms an A.P

• First term

• Common difference

• The sequence

EXPLANATION:

3 - 5n forms an A.P

When n = 1

The number will be 3 - 5(1) = 3 - 5 = - 2

when n = 2

The number will be 3 - 5(2) = 3 - 10 = - 7

when n = 3

The number will be 3 - 5(3) = 3 - 15 = - 12

We can notice the difference between the terms is - 5. Hence it forms an A.P.

First term:

When n = 1, it will be the first term.

a = 3 - 5(1) = 3 - 5 = - 2

Common difference:

d = t₂ - t₁

t₂ = 3 - 5(2) = 3 - 10 = - 7

t₁ = a = 3 - 5(1) = 3 - 5 = - 2

d = - 7 - (-2)

d = -7 + 2

d = - 5

The sequence:

-2 , -7 , - 12, - 17, - 22 ........

The sequence can be obtained by adding - 5 to the - 2 and to the number obtained as result (-7) and so on.

Answer 2

$\sf \red{ Question}$

• The algebraic expression of an arithmetic sequence is 3-5n?
• Find its common difference?
• Find its first term?
• Form a sequence ?

$\sf \orange{ Given}$

• The algebraic expression of an arithmetic sequence is 3-5n

$\sf \pink{ To \: find}$

• Find its common difference?
• Find its first term?
• Form a sequence ?

$\sf \purple{ solution}$

$\sf \red{ common \: difference }\\ \sf \: = - 7 - ( - 2) \\ \sf \: = - 7 + 2 \\ \sf \: = \orange{- 5} \\ \sf \red{first \: terms} \\ \sf \: \begin{lgathered} \sf \: a_{1} = 3 - 5(1) \\ \sf \: \: \: \: \: \: = \: 3 - 5 \\ \sf \: \: \: \: \: \green{ = - 2 }\\ \sf \: a_{2} =3 - 5(2) \\ \sf \: \: \: \: \: \: \pink{= - 7 }\\ \sf \purple{sequence }\\ \sf \: - 2. - 7. - 13. - 18\end{lgathered} \\ </p><p>$

Hence añswer